Answer
Foci :
$(-\displaystyle \frac{\sqrt{3}}{2},0)$ and $(\displaystyle \frac{\sqrt{3}}{2},0)$.
Work Step by Step
Write the equation in standard form:
$x^{2}=1-4y^{2}\qquad/+4y^{2}$
$x^{2}+4y^{2}=1$
$\displaystyle \frac{x^{2}}{1}+\frac{y^{2}}{\frac{1}{4}}=1$
Major axis parallel to the x-axis, horizontal,
$a=1, b=\displaystyle \frac{1}{2}$
Center: (0,0)
Vertices: $(h-a, k),\quad (h+a, k) $
$(-1, 0),\quad (1, 0) $
$c^{2}=1-\displaystyle \frac{1}{4}=\frac{3}{4}$
$c=\displaystyle \frac{\sqrt{3}}{2}$
Foci :
$(-\displaystyle \frac{\sqrt{3}}{2},0)$ and $(\displaystyle \frac{\sqrt{3}}{2},0)$.
